It is commendable that you want to have your child baptized but that is only part of the obligation.
The Church baptizes infants because the parents or guardians promise to:
- raise them as Catholic Christians, and
- teach them the faith as they grow.
The parents have a responsibility to educate and practice the faith with, and for, their children. If you don't live as Catholics then you can't impart what you believe into your children.
- Is there some obstacle to getting married in the Church?
- Why don't you work that out?
- Do you worship as part of a different Christian community?
— That part was unclear.
You could probably have your child baptized in a non-Catholic Christian church, if that is where you practice, [and they administer a valid Trinitarian baptism] but I would encourage you to consider giving yourselves and your children the fullness of the Catholic faith, because that is the Church that Jesus founded. (Matthew 16:13-19)
I have friends that moved here from Brazil, became serious about their faith, and then decided to seek an annulment from a first marriage back in Brazil. They then lived as brother and sister (still a family, but practicing chastity) until they worked it out. Today God is blessing their family in ways they never could have imagined.
Being Christian is a life-challenging undertaking and if it doesn't test you in hard ways, it really wouldn't be that serious or worth it. Jesus' sufferings and death were paid for a reason, and our response to that gift needs to be to do hard things — the right things, and then the blessings follow.
I suggest you talk more with the priest and find out more about what the possibilities are for your situation and how you can get married in the Church.